Math  /  Algebra

Question6.013. a2=2;d=1;an=18a_{2}=2 ; d=1 ; a_{n}=18 A. 15 B. 16 C. 17 D. 18 E. 19 6.014. a3=5,5;a1=1,5;an=11,5a_{3}=5,5 ; a_{1}=1,5 ; a_{n}=11,5 A. 6 B. 7 C. 8 D. 9 E. 10

Studdy Solution

STEP 1

1. We are dealing with arithmetic sequences.
2. The formula for the n n -th term of an arithmetic sequence is an=a1+(n1)d a_n = a_1 + (n-1)d .

_HIGH_LEVEL_APPROACH_ for Problem 6.013:
1. Identify the first term a1 a_1 using the given information.
2. Use the arithmetic sequence formula to find n n .

_HIGH_LEVEL_APPROACH_ for Problem 6.014:
1. Identify the common difference d d using the given terms.
2. Use the arithmetic sequence formula to find n n .

**Problem 6.013:**

STEP 2

STEP 3

We know a2=2 a_2 = 2 and the common difference d=1 d = 1 . Use the formula for the second term to find a1 a_1 :
a2=a1+(21)d a_2 = a_1 + (2-1)d 2=a1+1×1 2 = a_1 + 1 \times 1 2=a1+1 2 = a_1 + 1 a1=21 a_1 = 2 - 1 a1=1 a_1 = 1

STEP 4

Now use the formula for the n n -th term to find n n when an=18 a_n = 18 :
an=a1+(n1)d a_n = a_1 + (n-1)d 18=1+(n1)×1 18 = 1 + (n-1) \times 1 18=1+n1 18 = 1 + n - 1 18=n 18 = n
The value of n n is:
18 \boxed{18}
**Problem 6.014:**
STEP_1: We know a3=5.5 a_3 = 5.5 and a1=1.5 a_1 = 1.5 . Use these to find the common difference d d :
a3=a1+(31)d a_3 = a_1 + (3-1)d 5.5=1.5+2d 5.5 = 1.5 + 2d 5.51.5=2d 5.5 - 1.5 = 2d 4=2d 4 = 2d d=2 d = 2
STEP_2: Now use the formula for the n n -th term to find n n when an=11.5 a_n = 11.5 :
an=a1+(n1)d a_n = a_1 + (n-1)d 11.5=1.5+(n1)×2 11.5 = 1.5 + (n-1) \times 2 11.5=1.5+2n2 11.5 = 1.5 + 2n - 2 11.5=2n0.5 11.5 = 2n - 0.5 11.5+0.5=2n 11.5 + 0.5 = 2n 12=2n 12 = 2n n=6 n = 6
The value of n n is:
6 \boxed{6}

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